Road trip! NM to Yellowstone

Personnally, I prefer US 191 all the way from I-40 to Yellowstone. Takes you to Canyon de Chelly NM, Canyonlands NP, Moab, Arches NP, Vernal-Dinosaur NM, Flaming Gorge, Pinedale, Jackson, Grand Teton NP, Colter Bay's great campground, and the South Entrance to Yellowstone. Much more scenic than anywhere along I-15 and avoids SLC as well. You see the real West--desert, mesas, plateau, multiple mountain ranges, alpine forest, and the Colorado, Green, Snake, and Yellowstone Rivers--on that highway, not the "Interstate West."

And, if you haven't been there before, don't miss the Buffalo Bill Center of the West in Cody, WY. Plan on a whole day just for that as it has multiple museums.